Geodesic
On the Cauchy problem for hyperbolic functional-differential equations
Adrian Karpowicz1 ; Henryk Leszczyński1
1Institute of Mathematics University of Gdańsk 80-952 Gdańsk, Poland
Annales Polonici Mathematici, Tome 115 (2015) no. 1, pp. 53-74
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

Voir la notice de l'article

We consider the Cauchy problem for a nonlocal wave equation in one dimension. We study the existence of solutions by means of bicharacteristics. The existence and uniqueness is obtained in $W^{1,\infty }_{\rm loc}$ topology. The existence theorem is proved in a subset generated by certain continuity conditions for the derivatives.
DOI : 10.4064/ap115-1-5
Keywords: consider cauchy problem nonlocal wave equation dimension study existence solutions means bicharacteristics existence uniqueness obtained infty loc topology existence theorem proved subset generated certain continuity conditions derivatives

Adrian Karpowicz  1   ; Henryk Leszczyński  1

1 Institute of Mathematics University of Gdańsk 80-952 Gdańsk, Poland 
@article{10_4064_ap115_1_5,
     author = {Adrian Karpowicz and Henryk Leszczy\'nski},
     title = {On the {Cauchy} problem for hyperbolic functional-differential equations},
     journal = {Annales Polonici Mathematici},
     pages = {53--74},
     year = {2015},
     volume = {115},
     number = {1},
     doi = {10.4064/ap115-1-5},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4064/ap115-1-5/}
}
TY  - JOUR
AU  - Adrian Karpowicz
AU  - Henryk Leszczyński
TI  - On the Cauchy problem for hyperbolic functional-differential equations
JO  - Annales Polonici Mathematici
PY  - 2015
SP  - 53
EP  - 74
VL  - 115
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4064/ap115-1-5/
DO  - 10.4064/ap115-1-5
LA  - en
ID  - 10_4064_ap115_1_5
ER  - 
%0 Journal Article
%A Adrian Karpowicz
%A Henryk Leszczyński
%T On the Cauchy problem for hyperbolic functional-differential equations
%J Annales Polonici Mathematici
%D 2015
%P 53-74
%V 115
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4064/ap115-1-5/
%R 10.4064/ap115-1-5
%G en
%F 10_4064_ap115_1_5
Adrian Karpowicz; Henryk Leszczyński. On the Cauchy problem for hyperbolic functional-differential equations. Annales Polonici Mathematici, Tome 115 (2015) no. 1, pp. 53-74. doi: 10.4064/ap115-1-5

Cité par Sources :